The phrase "further infestation" means the continued or increased spread or growth of something harmful or unwanted, such as pests or diseases. Full definition
Advantage flea control kills fleas before they lay eggs and one treatment prevents further infestation for at least four weeks. (all-about-puppies.com)
They also need to have the fleas removed and then returned to an environment where they will be protected from further infestation. (vin.com)
You need to make sure that the kitten's environment is free from worms to avoid further infestation. (tinpaw.com)